The effect of fish on plankton dynamics : a theoretical analysis

We present an expansion of a classical minimal Daphnia–algae model to account for effects of fish as a top predator. Our analyses suggest that in most situations, the plankton should show hysteresis in response to predation pressure by fish. Thus, there exist two distinct regimes, one in which Daphnia is controlled (overexploited) by fish and phytoplankton biomass is high and another in which Daphnia is relatively unaffected (underexploited) by planktivores and algae are controlled by Daphnia. Switches from one regime to the other occur abruptly at a critical fish density. This is in line with field observations and experimental results. Our model predicts that the critical fish density for Daphnia collapse is higher in systems with higher ambient nutrient concentrations. The model also shows how intrinsic predator–prey oscillations in the planktonic system can facilitate the switch to the algal-dominated regime where Daphnia is controlled by fish. In terms of dynamical systems theory, this switch happens through a homoclinic bifurcation. In biological terms, Daphnia collapses due to food limitation and is subsequently overexploited by fish. This is indeed the sequence of mechanisms observed at the end of the spring clearwater phase in lakes where Daphnia is absent during the summer when the biomass of young-of-the-year planktivorous fish becomes high.